Multiplicative updates for convex optimization with non-negativity constraints

Many problems in neural computation and statistical learning involve optimizations with nonnegativity constraints. Examples include large margin classfication by support vector machines, density estimation in Bayesian networks, dimensionality reduction by nonnegative matrix factorization, and LTI filter estimation in acoustic echo cancellation. In this project, we have proposed a series of iterative algorithms where the optimization variables are multiplicatively updated from one iteration to another iteration. Those algorithms are very easy to implement and free of parameters to be tuned for convergence. And in practice, they converge fast to desirable solutions.

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